Predictive Modeling Applications in Actuarial Science

Chapter 6 - Frequency and Severity Models


Edward W. Frees | University of Wisconsin-Madison

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Many insurance data sets feature information about how often claims arise, the frequency, in addition to the claim size, the severity. This chapter introduces tools for handling the joint distribution of frequency and severity. Frequency-severity modeling is important in insurance applications because of features of contracts, policyholder behavior, databases that insurers maintain, and regulatory requirements. Model selection depends on the data form. For some data, we observe the claim amount and think about a zero claim as meaning no claim during that period. For other data, we observe individual claim amounts. Model selection also depends upon the purpose of the inference; this chapter highlights the Tweedie generalized linear model as a desirable option. To emphasize practical applications, this chapter features a case study of Massachusetts automobile claims, using out-of-sample validation for model comparisons.

Data R Demonstrations R Code
Generalized Linear Model: Example Generalized Linear Model: Example
Grouped Versus Individual Data Example Grouped Versus Individual Data Example
Massachusetts Automobile Example
Insample Data Summary Statistics Summary Statistics
OutSample Data Model Fitting Model Fitting
Out-of-Sample Validation Out-of-Sample Validation